Are those in Hebrews 6:4 who "crucify
the Son of God afresh" lost?

Question:

Are there similarities between the second and third seeds in the
parable of the sower and Hebrews 6:4 - there is no return in any case;
the person is lost.

Response:

Hebrews 6:4-6 is another one of those famous (or infamous) passages
that is generally misunderstood. The key portion is the participial
phrase in verse six anastaurountes heautois ton huion tou theou kai
paradeigmatizontes - "seeing they crucify to themselves the Son of
God afresh, and put him to an open shame" (KJV). The King James,
creatively ambiguous here as it often is, preserves the hint necessary
to translate correctly. For this phrase hangs on the two present tense
participles which are to be taken temporally = "while/as long
as they are crucifying". The idea is not that the people addressed by
Paul in the book of Hebrews are irretrievably lost. The problem is that
these believers, after such a good start, had, over the years, fallen
back into the Jewish rites still being practiced in Jerusalem pre-70
A.D. For believers in Jesus Christ, it was/is anathema to participate in
the Old Testament rituals of animal sacrifice, because these rituals
foreshadowed the coming sacrifice of the Messiah. Since Jesus had at
that point in time already died, and His death was and is effective for
our salvation once and for all, to continue to participate in these
rites was to, in effect, proclaim Christ's death of no practical effect,
to "crucify Him all over again", and to shame Him in the process. For if
believers don't respect His death on the cross, who will? Later, Paul
will encourage these wayward believers to abandon ritual Judaism
entirely, to "go outside the camp, bearing the disgrace He bore" and
choose the true sacrifice of praise and good works rather than the
obsolete rituals of the Law which Christ has now fulfilled
(Heb.12:11-15).

Paul is saying in these verses that true repentance must precede
restoration. As long as one is actively involved in a sin (in this case,
continuing to "pretend" through participation in animal sacrifice that
Christ had yet to die for us), confession is pointless. First, one must
stop sinning. Then repentance and confession will be acceptable to God.
Until these Jewish believers had made up there minds to stop
accommodating to their neighbors and committing such sacrilege against
the Lord who had already bought them with His blood, there could be no
hope of their restoration.

So this is a somewhat different thing than the "seed on the rock" or
the "seed in the weeds" in the parable of the sower which you reference
(on which see Peter's
Epistles #12: "the Parable of the Sower"). The "seed on the rock" is
definitely lost, for faith is abandoned in difficult times. The "seed in
the weeds" is choked in terms of faith, and little production results
(in my opinion, some of these may be saved, but one is certainly
"playing with fire" to go this route). The believers to whom Hebrews was
addressed were in definite danger of abandoning what they had achieved,
but the whole point of the epistle to the Hebrews is to help these
people cleanse their hearts from their false impressions and wrong
practices, and to help them return to a fully sanctified course of
spiritual growth. We will have to wait to find out how they responded,
but Paul had confidence that they would take his words to heart (cf.
Heb.6:9-10 directly following), something we all need to do whenever we
bump into teachings from the Word of Truth which convict us of following
an improper course.